Should My SEO Strategy Target Multiple Locations?

In short, the answer to this question is no. You want to make it clear to search engines what your site is about. If you optimize for too many locations, you run the risk of confusing the search engines and not ranking well for any of the keywords you're targeting. In other words, if your property is located in West Hollywood, you want to optimize your site for West Hollywood keywords. If your property is located in Northern Liberties, Philadelphia, that's the neighborhood you should optimize for on your site.

Of course, there may be exceptions to this rule. Suppose your property is located on the border of two neighborhoods? In that case, you might want to consider optimizing for the neighborhood that has the higher search volume, or the one that you're already ranking for. Perhaps your property address is Atlanta, GA, but really your community is located in the Sandy Springs area. In that case, you'd likely want to optimize for Sandy Springs as it'll drive more relevant traffic to your site.